1. Field of the Invention
This invention relates to a position control system which ensures accurate and stable position control of numerical-controlled machine tools.
2. Description of the Prior Art
Position control systems for numerical-controlled machines tools may be divided into systems of the type employing a closed loop servomechanism such, for example as shown in FIG. 1, and systems of the type using a semi-closed loop servo-mechanism such, for example, as shown in FIG. 2. In the closed loop system, a position detector 13 such as an inductosyn or the like is mounted on a moving part of a machine tool which is to be controlled, for example, a moving table 11, and detected positional information Q from the position detector 13 is negatively fed back to the side of a position controller 15 of a numerical control unit and provided via an A-D converter 17 to an adder 19, wherein commanded positional information P and the abovesaid detected positional information Q are compared to obtain a position error variable R. The position error variable R is applied via a position loop gain setting circuit 21 and a D-A converter 23 to a velocity amplifier 25 to cause it to drive a motor 27 so that the position error variable R is reduced to zero, driving a reduction gear 29 and a ball screw 31 to perform position control of the moving table 11. In the semi-closed loop system, the position of the moving part to be ultimately controlled is not detected directly, but instead an indirect position, for example, the rotational angle of a motor shaft, is detected by a resolver or like detector 33 and negatively fed back so that it may coincide with the commanded positional information P.
FIGS. 3 and 4 show, by way of example, block diagrams respectively corresponding to FIGS. 1 and 2, indicating a position loop gain K; a transfer function G.sub.1 (s) of a velocity controller including the characteristics of the velocity amplifier 25 and the motor 27; a transfer function G.sub.2 (s) of the mechanical system including the characteristics of the reduction gear 29, the ball screw 31 and the moving table 11, including the break angular frequencies; .omega..sub.V and .omega..sub.M of the velocity controller and the mechanical system, respectively; and a damping factor .zeta.. As will be seen from the block diagrams, the closed loop system includes mechanical elements in its closed loop and hence is capable of ultimately correcting a pitch error and a torsional error of the ball screw 31, permitting position control with higher accuracy than the semi-closed loop system. Therefore, the closed loop system has widely been used with a boring lathe, milling machine or machining center requiring high accuracy.
In relation to the block diagrams, the maximum value Kmax of the position loop gain K at which the closed loop is stable and at which the movement of the moving table 11 does not become oscillatory is, in the case of the closed loop system, determined by the smaller one of the break angular frequencies .omega..sub.V and .omega..sub.M of the transfer functions of the velocity controller and the mechanical system, as expressed by the following equation (1), whereas in the case of the semi-closed loop system, it is determined by the break angular frequency .omega..sub.V of the transfer function of the velocity controller, as expressed by the following equation (2): EQU Kmax=(1/n).times.Min(.omega..sub.V, .omega..sub.M) (1) EQU Kmax=.omega..sub.V /n (2)
where n is approximately equal to 5. In the case of the closed loop system, if .omega..sub.M &gt;&gt;.omega..sub.V, no problem occurs; but when .omega..sub.M &lt;.omega..sub.V, the maximum value Kmax of the position loop gain becomes smaller than that in the semi-closed system. Consequently, the closed loop system is inferior to the semi-closed loop system in terms of follow-up error, acceleration-deceleration distance and servo rigidity. In general, the break angular frequency .omega..sub.M of the transfer function of the mechanical system is given by ##EQU1## where K.sub.L is the rigidity of the mechanical system including the reduction gear and the ball screw and J.sub.L is a load inertia. Accordingly, in the case where the rigidity K.sub.L of the mechanical system is small and the load inertia J.sub.L is large, for example, as in the case of a turntable of a large-sized machining center, the break angular frequency f.sub.M (=.omega..sub.M /2.pi.) of the transfer function of the mechanical system, for example, may sometimes become 10 Hz or so, and the position loop gain K that can be used becomes small which makes stable and accurate position control difficult.
In a numerical-controlled machine tool of the closed loop system, a nonlinear element of the mechanical system, for instance, backlash of a gear or nonlinear friction of a sliding surface enters into the closed loop, so that the movement of the moving table 11 is subjected to the influence of such a nonlinear element.
FIGS. 5A, 5B, 6A and 6B are graphs showing how the movement y of the moving table 11 and the position error variable R vary in dependence on whether the nonlinear element, for example, backlash having a magnitude D, occurs or not in the case of applying, as the commanded positional information P, a ramp input bearing the following relationship: EQU P=F.times.t (4)
where F is a feedrate and t is time. When no backlash occurs, the movement y of the moving table 11 follows up the input P only with an error corresponding to a steady velocity error variable .epsilon..sub.D (.epsilon..sub.D .varies. F/K), as depicted, for example, in FIG. 5A, and the position error variable R in such a case is as shown in FIG. 5B. When the backlash occurs, the movement y of the moving table 11 follows up the input P with an error F.times.t.sub.D, where t.sub.D is the time in which the backlash occurs, corresponding to the magnitude D of the backlash in addition to the steady velocity error variable .epsilon..sub.D, as shown in FIG. 6A, and the position error variable R in this case is as depicted in FIG. 6B. In this way, when the backlash occurs, the follow-up error increases as compared with the case of no backlash occurring.
In continuous cutting control adopted, for example, in an NC milling machine, NC lathe and so forth, when backlash acts on one of two simultaneously driven axes, for example, the X axis, with no backlash on the Y axis, even if the gain characteristics of the both axes are linear and equal to each other, the movement y of the moving table 11 gets out of its commanded locus L to introduce the corresponding machining error, as shown in FIG. 7. Such a machining error is also caused by nonlinear elements other than the backlash.
As described above, the conventional closed-loop type position control system for the numerical-controlled machine tool has the defect that a machining error is produced by the nonlinear elements of the mechanical system; furthermore, when the resonance frequency of the mechanical system, that is, the break angular frequency f.sub.M of the transfer function of the mechanical system, then the magnitude of the position loop gain that can be assumed within its stable region is limited, which results in the defect of a severe limitation on the position control accuracy and stability.